Optical device using a hollow-core photonic bandgap fiber

ABSTRACT

An optical device includes a hollow-core photonic-bandgap fiber, wherein at least a portion of the hollow-core photonic-bandgap fiber has a longitudinal axis and is twisted about the longitudinal axis.

CLAIM OF PRIORITY

The present application is a continuation of U.S. patent applicationSer. No. 11/681,073, filed Mar. 1, 2007, incorporated in its entirety byreference herein and which claims the benefit of U.S. Provisional PatentApplication No. 60/778,230, filed Mar. 2, 2006, which is incorporated inits entirety by reference herein.

BACKGROUND OF THE INVENTION

1. Field of the Invention

This application relates generally to the field of polarizationcontrollers for fiber optic applications.

2. Description of the Related Art

In hollow-core photonic-bandgap fibers (PBFs), the majority of thefundamental mode power propagates in air (see, e.g., specifications forHC-1550-02 hollow-core photonic-bandgap fiber available from CrystalFibre A/S of Birkerød, Denmark). This property makes hollow-core fiberspromising for a number of applications, including those in which highpeak powers and/or low nonlinearity are desired.

In general, it is desirable to be able to control the state ofpolarization (SOP) of light propagating in a fiber, and currently nosuch means exist in hollow-core fibers. In conventional single-modefibers (SMFs), polarization control is routinely achieved by bending thefiber into loops to induce birefringence through strain (see, e.g., H.C. Lefevre, “Single mode fractional wave devices and polarisationcontrollers,” Electronics Letters, Vol. 16, pages 778-780 (1980)). FIG.1 schematically illustrates an SMF bent to form a pair of loops having aradius of curvature R. The induced birefringence Δn is inverselyproportional to the square of the radius of curvature (i.e., Δn∝1/R²).The total phase delay δ_(l) produced by the loops is proportional to thenumber of loops N_(loops) divided by the radius of curvature of theloops (i.e., δ_(l)∝N_(loops)/R). For an SMF28 fiber, a quarter-waveplate can be produced using two loops each having a radius of curvatureof about 2.5 centimeters. Two such quarter-wave plates can be used as atrue universal polarization controller to transform any input state ofpolarization (SOP) into any output SOP. Such a polarization controllercan be described as transforming any input SOP to an output SOP thatreaches any point on the Poincaré sphere by both rotating the SOP andchanging its ellipticity.

SUMMARY OF THE INVENTION

In certain embodiments, a polarization controller is provided. Thepolarization controller comprises a first hollow-core photonic-bandgapfiber, wherein at least a portion of the first hollow-corephotonic-bandgap fiber has a first longitudinal axis and is twistedabout the first longitudinal axis.

In certain embodiments, a polarization controller is provided. Thepolarization controller comprises a hollow-core photonic-bandgap fiber,wherein at least a portion of the hollow-core photonic-bandgap fiber hasa longitudinal axis and is twisted about the longitudinal axis.

In certain embodiments, a method of modifying a state of polarization ofan optical signal is provided. The method comprises providing an opticalsignal having a first state of polarization. The method furthercomprises propagating the optical signal through at least a portion of ahollow-core photonic-bandgap fiber having a longitudinal axis andtwisted about the longitudinal axis. The optical signal is outputtedfrom the twisted portion of the hollow-core photonic-bandgap fiber witha second state of polarization different from the first state ofpolarization.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 schematically illustrates a single-mode fiber bent to form a pairof loops having a radius of curvature R.

FIG. 2 schematically illustrates a birefringent fiber viewed as acollection of wave plates, each plate having a linear phase delay δ_(l),a circular phase delay δ_(c), and a birefringence axes orientation θ.

FIGS. 3A and 3B illustrate the Poincaré spheres (for on-axis input andoff-axis input, respectively) for a configuration in which a fiber has alength much greater than the beat length of the fiber.

FIGS. 4A and 4B illustrate the Poincaré spheres (for on-axis input andoff-axis input, respectively) for a configuration in which a fiber has alength much less than the beat length of the fiber.

FIGS. 5A and 5B illustrate the Poincaré spheres (for on-axis input andoff-axis input, respectively) for a portion of a hollow-corephotonic-bandgap fiber having a length approximately equal to the beatlength of the portion of the hollow-core photonic-bandgap fiber.

FIG. 6 schematically illustrates an example polarization controller inaccordance with certain embodiments described herein.

FIG. 7 illustrates the various output polarizations on the Poincarésphere for variations of the twist angle r of the hollow-corephotonic-bandgap fiber of FIG. 6.

FIG. 8 schematically illustrates another example polarization controllercompatible with certain embodiments described herein.

FIG. 9 schematically illustrates an example polarization controller inwhich the twisted portions of the first hollow-core photonic-bandgapfiber and the second hollow-core photonic-bandgap fiber are opticallycoupled together without a single-mode fiber therebetween.

FIG. 10 schematically illustrates another example polarizationcontroller in accordance with certain embodiments described herein.

FIG. 11 illustrates a non-zero net alignment of birefringent axes due totwisting of a fiber.

FIG. 12 schematically illustrates a configuration to twist at least aportion of a hollow-core photonic-bandgap fiber between two fixedportions and measure the effects on the state of polarization of asignal traversing the twisted portion of the hollow-corephotonic-bandgap fiber.

FIG. 13A illustrates the evolution of the output state of polarizationfor incrementally larger twists applied to the twisted portion of thehollow-core photonic-bandgap fiber.

FIG. 13B illustrates the results of a calculated model of the evolutionof the output state of polarization for the configuration of FIG. 12.

FIG. 14A schematically illustrates a polarization controller comprisinga twisted portion of a first hollow-core photonic-bandgap fiber, atwisted portion of a second hollow-core photonic-bandgap fiber, and atwisted portion of a third hollow-core photonic-bandgap fiber.

FIG. 14B schematically illustrates the configuration of FIG. 12 used tomeasure the effects of the polarization controller of FIG. 14A.

FIG. 15 is a flow diagram of an example method for modifying thepolarization of an optical signal in accordance with certain embodimentsdescribed herein.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENT

Most of the light mode propagating through a conventional single-modefiber (SMF) travels through the silica of the SMF. A conventional SMFhas a low intrinsic birefringence, but has a large birefringence inducedby bending the SMF. Thus, a loop polarization controller using aconventional SMF works well.

In contrast, a hollow-core photonic-bandgap fiber (PBF) is not readilyamenable to polarization control by this method. Most of the modepropagating through the hollow-core PBF travels in the strain-freehollow core. Such hollow-core PBFs have a high intrinsic birefringence,but only a small birefringence induced by bending. For example, there isno measurable difference in the induced birefringence of a hollow-corePBF bent with a radius of curvature of 10 centimeters and one bent witha radius of curvature of 1.5 centimeters. Thus, a loop polarizationcontroller using a hollow-core PBF is not practical because the effectsof strain due to bending are too small. As used herein, the term“hollow-core” is used in its broadest sense and includes configurationsin which the fiber has a hollow core filled with air or any gas orcombination of gases at atmospheric pressure or any other pressure. Asused herein, the term “fiber” is used in its broadest sense and includesa complete length of fiber or a fractional portion or segment of a fiberencompassing one end, two ends, or neither end of the fiber.

To understand the effects of axially twisting a fiber on itsbirefringence, the simple case of twisting the free end of abirefringent fiber can be considered. One portion (e.g., end) of thefiber is attached to a support located a short distance L from itsoutput end, and the output end is twisted by an angle τ. A birefringentfiber may be viewed as a collection of wave plates, each plate having alinear phase delay δ_(l), a circular phase delay δ_(c), and abirefringence axes orientation θ, as schematically illustrated by FIG.2. Linear birefringence causes the linear phase delay δ_(l) betweenorthogonal linear polarizations. For example, a quarter-wave linearbirefringent plate at 45° to a linearly polarized signal causes a phasedelay of π/2 radians, thereby changing the state of polarization of thesignal from being linearly polarized signal to being circularlypolarized. Circular birefringence causes the circular phase delay δ_(c)between opposite (e.g., left and right) circular polarizations. Forexample, a quarter-wave circular birefringent plate causes a phase delayof π/2 radians, thereby changing a 45° linear polarization to ahorizontal linear polarization.

When the fiber end is twisted, two mechanisms contribute to altering itsbirefringence. First, the fiber experiences a shear strain due to thetwisting, which induces a circular phase delay proportional to theamount of twist. In a conventional single-mode fiber, the magnitude ofthis strain-induced circular phase delay is small (e.g., δ_(c)=−gτ, withg=0.13-0.16). For example, in a typical conventional fiber, a twist of180° produces less than 15° of polarization rotation. Previously, Ulrichand Simon (R. Ulrich and A. Simon, “Polarization optics of twistedsingle-mode fibers,” Appl. Opt., Vol. 18, pages 2241-2251 (1979))proposed axially twisting a short length of SMF in its middle to utilizethis effect to produce a fast-slow mode interchanger.

Second, axially twisting a fiber alters its birefringence by reorientingthe axis of intrinsic linear birefringence along the twisted section ofthe fiber, causing a circular birefringence. Thus, the orientation θchanges for each plate such that the axes of the individual wave platesare rotated relative to each other. The magnitude of this effect dependson the ratio of the length L of the twisted portion to the beat lengthL_(b) of the fiber. The beat length is the length over which twoorthogonally polarized signals, initially in phase, passes in order toachieve a 2π radians phase difference between the two signals, and thebeat length can be wavelength-dependent. If L>>L_(b), (e.g., a10-centimeter segment of a conventional polarization-maintaining (PM)fiber with a beat length L_(b)=5 millimeters), twisting will alter thesignal SOP by large amounts relative to the input SOP, but theellipticity of the output SOP does not change. FIGS. 3A and 3Billustrate the Poincaré spheres for such a configuration for on-axisinput and off-axis input, respectively. For on-axis input (FIG. 3A), thepolarization follows the twisted fiber axis and never moves towards thepoles. For off-axis input (FIG. 3B), beating is obtained. Such a devicetherefore fails to act as a true universal polarization controller.

In the other extreme limit of L<<L_(b), (e.g., a 10-centimeter segmentof a conventional low-birefringence SMF with a beat length of 1 meter),once the amount of twist exceeds a few degrees, the twist-inducedcircular birefringence far exceeds the intrinsic linear birefringence.The fiber then acts as a nearly pure circular birefringent element.FIGS. 4A and 4B illustrate the Poincaré spheres for such a configurationfor on-axis input and off-axis input, respectively. In both cases, ifthe length of the twisted section of the fiber is much less than a beatlength of the fiber, the polarization does not change much since thereis little phase delay in the twisted section. Again, such a devicecannot change the ellipticity of the output SOP and cannot perform as apolarization controller.

In contrast to these two extreme cases, a twisted fiber portion can be auseful polarization controller if the length of the twisted portion isof the order of the beat length (L≈L_(b)). As the portion is twisted,both the orientation and ellipticity of the output SOP are modified. Thecondition L≈L_(b) cannot be met in practice for either a PM fiber(twisting a 5-millimeter long fiber requires a large torque that mightbreak the fiber) or a standard SMF (which would require twisting arather long fiber). This is one reason why such an approach is not usedwith conventional fibers.

In a hollow-core fiber, very little power propagates in the silicaregions where the strain is present, so the strain-induced circularphase delay is negligible and certainly smaller than in a conventionalSMF. The main effect of an axial twist of a hollow-core PBF is to rotatethe individual wave plates with respect to each other. Furthermore,since the linear birefringence of a hollow-core PBF is much greater thanthat of a conventional SMF such that the beat length of a hollow-corefiber is smaller than that of a conventional SMF (e.g., typically in arange between 1 centimeter and 10 centimeters) (See, e.g., M. Wegmulleret al., “Experimental investigation of the polarization properties of ahollow core photonic bandgap fiber for 1550 nm,” Opt. Express, Vol. 13,pages 1457-1467 (2005); G. Bouwmans et al., “Properties of a hollow-corephotonic bandgap fiber at 850 nm wavelength,” Opt. Express, Vol. 11,pages 1613-1620 (2003); M. S. Alam et al., “High group birefringence inair-core photonic bandgap fibers,” Opt. Express, Vol. 30, pages 824-826(2005).) In certain embodiments, axially twisting one or more portionsof a hollow-core PBF can induce significant changes to the polarizationfor both on-axis and off-axis input, as illustrated by FIGS. 5A and 5B,respectively. Certain embodiments described herein use this behavior tomake a practical polarization controller in which the desired SOP isachieved by varying the amount of twist.

Certain embodiments described herein provide an alternative method forpolarization control in hollow-core fibers using one or more twistedportions of fiber. Twisting a portion of a fiber between two fixedpoints spaced by about one beat length can significantly alter theoutput polarization orientation and ellipticity of the light propagatingthrough the twisted portion of the hollow-core fiber, and can thus beused to control polarization for hollow-core fibers. Measurements of thepolarization produced by certain embodiments described herein are ingood agreement with a model based on the Jones matrix formalism. Thisprinciple can be used to demonstrate a simple, short, and effectivepolarization controller in a hollow-core fiber comprising three shortsections of twisted fiber. In certain embodiments, the polarizationcontroller performs with a 20-dB extinction ratio such that about 99% ofthe optical power is in the desired polarization.

FIG. 6 schematically illustrates an example polarization controller 10in accordance with certain embodiments described herein. Thepolarization controller 10 comprises a hollow-core photonic-bandgapfiber (PBF) 20 wherein at least a portion of the hollow-core PBF 20 hasa longitudinal axis 30 and is twisted about the longitudinal axis 30.While FIG. 6 schematically illustrates an embodiment in which thetwisted portion of the hollow-core PBF 20 is at one end of thehollow-core PBF 20, in certain other embodiments, the twisted portion isbetween two fixed portions (e.g., the ends) of the hollow-core PBF 20,as discussed below with regard to FIG. 10. In certain embodiments, theportion of the hollow-core PBF 20 to be twisted is affixed to a rotationstage or a loop-type polarization controller (e.g., using epoxy or wax)and fixed portions of the hollow-core PBF 20 are affixed to stationarystructures (e.g., using epoxy, wax, or mechanical clamps). Personsskilled in the art are able to affix one or more portions of thehollow-core PBF 20 to stationary and rotatable structures as appropriateto twist at least a portion of the hollow-core PBF 20 in accordance withcertain embodiments described herein.

A polarization controller changes an input polarization into a differentoutput polarization, and in certain embodiments, into many differentoutput polarizations. As described herein, the twisting of at least aportion of the hollow-core PBF 20 by different amounts gives rise tochanges of the output polarization for a fixed input polarization. Thebehavior of a twisted birefringent fiber can be quantified with theJones matrix formalism. The Jones matrix of a twisted birefringent fiberis governed by three parameters: the fiber's intrinsic linear phasedelay δ_(l), the circular phase delay δ_(c) (which is the sum of theintrinsic and strain-induced circular phase delays), and the twist angleτ. In the basis of the fiber's principal axes, the Jones matrix M for atwisted birefringent fiber is given by Equation (1):

$M = \begin{pmatrix}P & {- Q^{*}} \\Q & P^{*}\end{pmatrix}$ where P = cos (Δ) − i(δ_(l)/2)sin (Δ)/Δ;Q = (τ + δ_(c)/2)sin (Δ)/Δ; andΔ = ((δ_(l)/2)² + (τ + δ_(c)/2)²)^(1/2).

These equations apply to any optical fiber (conventional low- orhigh-birefringent fibers and hollow-core fibers). In a hollow-corefiber, since the strain-induced circular birefringence is negligible,δ_(c) is just the intrinsic circular birefringence. As illustrated byFIG. 7, by varying the twist angle τ of the twisted portion of thehollow-core PBF 20 of FIG. 6, the output polarization can be variedsignificantly. In certain embodiments, the twisted portion of thehollow-core PBF 20 has a length approximately equal to a beat length ofthe twisted portion of the hollow-core PBF 20.

FIG. 8 schematically illustrates another example polarization controller100 compatible with certain embodiments described herein. Thepolarization controller 100 comprises at least a portion of a firsthollow-core PBF 110 and at least a portion of a second hollow-core PBF120 optically coupled to the portion of the first hollow-core PBF 110.The portion of the first hollow-core PBF 110 has a first longitudinalaxis 112 and is twisted about the first longitudinal axis in a firstdirection. The portion of the second hollow-core PBF 120 has a secondlongitudinal axis 122 and is twisted about the second longitudinal axis122 in a second direction.

In certain embodiments, the second longitudinal axis 122 issubstantially parallel to the first longitudinal axis 112, while incertain other embodiments, the second longitudinal axis 122 is notsubstantially parallel to the first longitudinal axis 112. At least oneof the twisted portion of the first hollow-core PBF 110 and the twistedportion of the second hollow-core PBF 120 can be curved or bent suchthat either or both of the longitudinal axes 112, 122 are not straightlines. In certain embodiments, the second direction is generallyopposite to the first direction, as schematically illustrated by FIG. 8.The twisted portion of the first hollow-core PBF 110 in certainembodiments has a length approximately equal to a first beat length ofthe twisted portion of the first hollow-core PBF 110. The twistedportion of the second hollow-core PBF 120 in certain embodiments has alength approximately equal to a second beat length of the twistedportion of the second hollow-core PBF 120.

As schematically illustrated by FIG. 8, in certain embodiments, thepolarization controller 100 further comprises a single-mode fiber (SMF)130 positioned between and optically coupled to the twisted portions ofthe first hollow-core PBF 110 and the second hollow-core PBF 120. Thetwisted portion of the first hollow-core PBF 110 comprises or is at anend of the first hollow-core PBF 110 which is coupled to the SMF 130 andthe twisted portion of the second hollow-core PBF 120 comprises or is atan end of the second hollow-core PBF 120 which is coupled to the SMF130. While twisting the hollow-core PBFs 110, 120 changes thepolarization of the transmitted light significantly, twisting the SMF130 has little or no effect on the polarization.

FIG. 9 schematically illustrates an example polarization controller 100in which the twisted portion of the first hollow-core PBF 110 and thetwisted portion of the second hollow-core PBF 120 are optically coupledtogether without the SMF 130 therebetween. The twisted portion of thefirst hollow-core PBF 110 is between two fixed portions 126 of the firsthollow-core PBF 110. The twisted portion of the second hollow-core PBF120 is between two fixed portions 126 of the second hollow-core PBF 120.In certain embodiments, the fixed portions 126 of the first hollow-corePBF 110 comprise two ends of the first hollow-core PBF 110 and the fixedportions 126 of the second hollow-core PBF 120 comprise two ends of thesecond hollow-core PBF 120, one of which is coupled to an end of thefirst hollow-core PBF 110, as schematically illustrated by FIG. 9. Incertain other embodiments, the first hollow-core PBF 110 and the secondhollow-core PBF 120 are the same hollow-core PBF.

In certain embodiments, the second longitudinal axis 122 issubstantially parallel to the first longitudinal axis 112. In certainembodiments, the second direction is generally opposite to the firstdirection, as schematically illustrated by FIG. 9. By combining multipletwisted portions of one or more hollow-core PBFs, certain embodimentsdescribed herein can transform arbitrary input polarization into anarbitrary desired output polarization by varying the amount of twist.

FIG. 10 schematically illustrates another example polarizationcontroller 200 in accordance with certain embodiments described herein.The polarization controller 200 comprises at least a portion of ahollow-core PBF 210 between two fixed portions 216 (e.g., two fixedends) of the hollow-core PBF 210. The portion of the hollow-core PBF 210has a longitudinal axis 220 and is twisted about the longitudinal axis220. A twisted portion 212 of the hollow-core PBF 210 is twisted by anamount +τ, and a portion 214 of the hollow-core PBF 210 between the twofixed portions 216 is twisted by an amount −τ.

The embodiment schematically illustrated by FIG. 10 can be expressedusing the Jones matrix formalism. The Jones matrix for such a twistedfiber is the product of two matrices M₊ and M⁻ of the form given inEquation (1). M₊ is the Jones matrix of the first twisted portion 212 ofthe hollow-core PBF 210 (twisted by +τ), and M⁻ is the Jones matrix ofthe second twisted portion 214 of the hollow-core PBF 210 (twisted by−τ). The portion 212 twisted by an amount +τ can be expressed byEquation (2):

$M_{+} = \begin{pmatrix}P & {- Q^{*}} \\Q & P^{*}\end{pmatrix}$ where P = cos (Δ) − i(δ_(l)/2)sin (Δ)/Δ;Q = (τ + δ_(c)/2)sin (Δ)/Δ; andΔ = ((δ_(l)/2)² + (τ + δ_(c)/2)²)^(1/2).

The portion 214 twisted by an amount −τ can be expressed by Equation(3):

$M_{-} = \begin{pmatrix}P^{\prime} & {- {Q^{\prime}}^{*}} \\Q^{\prime} & {P^{\prime}}^{*}\end{pmatrix}$ whereP^(′) = cos (Δ^(′)) − i(δ_(l)/2)sin (Δ^(′))/Δ^(′);Q^(′) = (τ + δ_(c)/2)sin (Δ^(′))/Δ^(′); andΔ^(′) = ((δ_(l)/2)² + (−τ + δ_(c)/2)²)^(1/2).

Equations (2) and (3) illustrate mathematically that the Jones matricesM₊ and M⁻ are not inverses of one another. For the Jones matrices M₊ andM⁻ to be inverses of one another, the conditions P′=P* and Q′=−Q wouldhave to apply since M₊ is unitary. Therefore, the polarization changesby the first portion 212 and by the second portion 214 formed bytwisting the fiber between two fixed portions 216, as schematicallyillustrated by FIG. 10, do not cancel each another out. This behaviorcan be understood physically by realizing that there is a non-zero netalignment of birefringent axes due to the twist, as schematicallyillustrated by FIG. 11, and such a twisted element does alter the SOPsignificantly. A polarization controller can then be constructed byconcatenating one or more twistable portions along the hollow-core PBF.

FIG. 12 schematically illustrates a configuration 300 to twist at leasta portion of a hollow-core PBF 210 between two fixed portions 216 andmeasure the effects on the SOP of a signal traversing the hollow-corePBF 210 (e.g., a 20-centimeter strand of HC-1550-02 available fromCrystal Fibre A/S of Birkerød, Denmark). A laser source 310 (e.g., alaser generating light having a wavelength of about 1545 nanometers,such as Model D2525P41 available from Lucent Technologies Inc.) isequipped with a laser mount to control the temperature of the laser(e.g., Newport 740 Series laser mount) optically coupled to thehollow-core PBF 210 via a first SMF 320 (e.g., SMF28 available fromCorning, Inc. of Corning, N.Y.) and a first polarizer 330. Examples oflasers compatible with certain embodiments described herein include, butare not limited to, diode lasers and tunable lasers. Examples ofpolarizers compatible with certain embodiments described herein include,but are not limited to, Model 10GT04 available from Newport Corporationof Irvine, Calif. The first polarizer 330 can be adjusted to introducelight to the hollow-core PBF 210 having a selected input polarization.The output of the hollow-core PBF 210 is optically coupled to a powermeter 360 via a second polarizer 340 and a second SMF 350. The secondpolarizer 340 can be adjusted to select the output polarization which ismeasured by the power meter 360. Examples of power meters compatiblewith certain embodiments described herein include, but are not limitedto, Model 8509B lightwave polarization analyzer system available fromAgilent Technologies, Inc. of Santa Clara, Calif. In certainembodiments, the second SMF 350 is butt-coupled to the output end of thehollow-core PBF 210. The second SMF 350 advantageously filters out anysurface modes and any higher-order modes.

For a given linear input SOP, FIG. 13A illustrates the evolution of theoutput SOP for incrementally larger twists applied to at least a portionof the hollow-core PBF 210, first a positive twist up to 180°, then anegative twist up to −180°, recording the measured power for every 15°of twist. As the hollow-core PBF 210 is twisted, the range of outputpolarizations subtends a substantial portion of the Poincaré sphere. Themeasurements illustrated by FIG. 13A show that when twisting ahollow-core PBF 210, both the orientation and ellipticity of the outputSOP are modified substantially. The output polarization evolves on asubstantial path on the Poincaré sphere, so the twisted portion of thehollow-core PBF 210 can be used as a polarization controller. Inaddition, FIG. 13A illustrates an asymmetry between positive andnegative twists of the hollow-core PBF 210.

FIG. 13B illustrates the results of a calculated model of the evolutionof the output SOP for the configuration of FIG. 12. To compare themeasured data of FIG. 13A with the model, it was assumed that δ_(l) andδ_(c) were uniform, thus the same values of δ_(l) and δ_(c) were used inM₊ and M⁻. The parameters used to fit the simulations to theexperimental data were the angle of the fiber principal axes in thelaboratory frame and the intrinsic phase delays δ_(l) and δ_(c), bothassumed to be independent of the twist. Additionally, a small linearbirefringence (total phase delay of 0.6 radians) and its orientationwere fitted to account for the birefringence of the hollow-core PBF 210and the SMF28 fiber output leads. Comparison to FIG. 13A shows that theexperimental and simulated results are in good qualitative agreement,including the asymmetry for positive and negative twists. The fittedvalues of δ_(l) (−22.6 radians) and δ_(c) (−6.6 radians) are inreasonable agreement with independent measurements of the birefringenceof the hollow-core PBF 210 (linear beat length of 6.5±1.5 centimeters,and circular beat length about 6 times longer). The slight disagreementthat occurs when the fiber is twisted most likely originates from theassumptions that (1) δ_(l) and δ_(c) are uniform, which have beenobserved experimentally not to be quite true, and (2) the twist does notaffect the fiber's native linear and circular birefringence, which maybe incorrect since twisting likely warps the photonic-crystal lattice ofthe twisted portion of the hollow-core PBF 210.

FIG. 14A schematically illustrates a polarization controller 400comprising a first twisted portion of a hollow-core PBF 410, a secondtwisted portion of a hollow-core PBF 420 optically coupled to the firsttwisted portion of the hollow-core PBF 410, and a third twisted portionof a hollow-core PBF 430 optically coupled to the twisted portion of thesecond hollow-core PBF 420. Each of the twisted portions of thehollow-core PBFs 410, 420, 430 is between two fixed portions 440 of thepolarization controller 400. FIG. 14B schematically illustrates theconfiguration 300 of FIG. 12 used to measure the effects of thepolarization controller 400.

The twisted portion of the third hollow-core PBF 430 of certainembodiments has a third longitudinal axis and is twisted about the thirdlongitudinal axis. In certain embodiments, the first longitudinal axis,the second longitudinal axis, and the third longitudinal axis aresubstantially parallel to one another, while in certain otherembodiments, at least one of the longitudinal axes is not substantiallyparallel to either of the other two longitudinal axes. At least one ofthe twisted portions of the hollow-core PBFs 410, 420, 430 can be curvedor bent such that the corresponding longitudinal axes are not straightlines. In certain embodiments, the hollow-core PBFs 410, 420, 430 arethe same hollow-core PBF.

As shown in FIG. 14A, the twisted portion of the first hollow-core PBF410 is twisted in a first direction about the first longitudinal axis,the twisted portion of the second hollow-core PBF 420 is twisted in asecond direction about the second longitudinal axis, and the twistedportion of the third hollow-core PBF 430 is twisted in a third directionabout the third longitudinal axis. The third direction of certainembodiments is generally opposite to the second direction and the seconddirection of certain embodiments is generally opposite to the firstdirection.

In certain embodiments, the twisted portion of the first hollow-core PBF410 has a length approximately equal to a first beat length of thetwisted portion of the first hollow-core PBF 410, the twisted portion ofthe second hollow-core PBF 420 has a length approximately equal to asecond beat length of the twisted portion of the second hollow-core PBF420, and the twisted portion of the third hollow-core PBF 430 has alength approximately equal to a third beat length of the twisted portionof the third hollow-core PBF 430. In certain embodiments, the first beatlength, the second beat length, and the third beat length areapproximately equal to one another. In certain other embodiments, atleast one of the first, second, and third beat lengths is not equal tothe other beat lengths. In certain other embodiments, none of the first,second, and third beat lengths are equal to one another.

The twisted portion of the first hollow-core PBF 410 can comprise an endof the first hollow-core PBF 410. The twisted portion of the secondhollow-core PBF 420 can comprise an end of the second hollow-core PBF420. The twisted portion of the third hollow-core PBF 430 can comprisean end of the third hollow-core PBF 430. The twisted portion of thefirst hollow-core PBF 410 can be between a first fixed portion and asecond fixed portion of the first hollow-core PBF 410. The twistedportion of the second hollow-core PBF 420 can be between a first fixedportion and a second fixed portion of the second hollow-core PBF 420.The twisted portion of the third hollow-core PBF 430 can be between afirst fixed portion and a second fixed portion of the third hollow-corePBF 430. One or more of the fixed portions of the first, second, andthird hollow-core PBFs 410, 420, 430 can be at the ends of thecorresponding hollow-core PBFs 410, 420, 430.

In certain embodiments, each of the twisted portions of the hollow-corePBFs 410, 420, 430 has a length in a range between 4 centimeters and 6.5centimeters, although other lengths are also compatible with certainembodiments described herein. For example, the same hollow-core PBF canbe held at four positions to form three 6-centimeter-long segments to betwisted. By adjusting the amount of twist in each of the hollow-corePBFs 410, 420, 430, various input SOPs can be transformed into variouslinear, circular, and elliptical target output SOPs. Random variation ofthe twist angle in each of the three segments of certain embodimentsproduces an output SOP that covers the entire Poincaré sphere. Similarresults can be obtained for random variations of the input SOP,confirming that the set of three twisted PBF sections constitutes auniversal polarization controller. In addition, there are no indicationsthat insertion loss or polarization dependent loss of the fiber aresignificant effects in certain embodiments of the polarizationcontroller described herein. In certain embodiments, at least 20 dB ofextinction can be achieved between the target output SOP and the SOPorthogonal to the target output SOP. Certain other embodiments furthercomprise additional twisted portions of one or more hollow-core PBFswhich can be twisted to improve the extinction of the polarizationcontroller.

Since the phase delay accumulated by two orthogonally polarized signalsas they travel through a fiber depends on wavelength, in general, twosignals with different wavelengths but the same polarization will exit afiber with different polarizations. This effect can limit the wavelengthrange that can be simultaneously controlled by a given polarizationcontroller. In certain embodiments, the bandwidth of the polarizationcontroller operating at a wavelength of about 1550 nanometers is about 6nanometers for control to within 5% of the same SOP, such that outsidethis bandwidth, less than 95% of the power is in the desired SOP at theoutput. In contrast, a conventional loop polarization controller has abandwidth of about 150 nanometers. One reason for this difference isthat the birefringence of the PBF decreases with wavelength, whichreduces the bandwidth. If the birefringence did not change withwavelength, greater bandwidths can be achieved. If the birefringence isproportional to the wavelength, greater bandwidths can be achieved.Another reason is that a conventional fiber polarization controller ismade from three quarter-wave sections of fiber, while the twist-basedpolarization controller of certain embodiments utilizes three sectionsthat are each one beat length long. However, in spite of its smallbandwidth, a twist-based PBF polarization controller in accordance withcertain embodiments described herein is a useful device for controllingthe SOP of laser light.

FIG. 15 is a flow diagram of an example method 500 for modifying thepolarization of an optical signal in accordance with certain embodimentsdescribed herein. In an operational block 510, the method 500 comprisingproviding an optical signal having a first state of polarization. In anoperational block 520, the method 500 further comprises propagating theoptical signal through at least a portion of a hollow-corephotonic-bandgap fiber having a longitudinal axis and twisted about thelongitudinal axis such that the optical signal is outputted from thetwisted portion of the hollow-core photonic-bandgap fiber with a secondstate of polarization different from the first state of polarization. Incertain embodiments, the method 500 further comprises an operationalblock 530 in which an amount of twisting of the twisted portion of thehollow-core photonic-bandgap fiber about the longitudinal axis is variedto select the second state of polarization.

Various embodiments of the present invention have been described above.Although this invention has been described with reference to thesespecific embodiments, the descriptions are intended to be illustrativeof the invention and are not intended to be limiting. Variousmodifications and applications may occur to those skilled in the artwithout departing from the true spirit and scope of the invention asdefined in the appended claims.

1. An optical device comprising: a first hollow-core photonic-bandgapfiber configured to transmit light having a wavelength, wherein at leasta portion of the first hollow-core photonic-bandgap fiber has a firstlongitudinal axis and is twisted about the first longitudinal axis alonga first beat length of the twisted portion of the first hollow-corephotonic-bandgap fiber, the first beat length dependent on thewavelength.
 2. The device of claim 1, wherein the twisted portion of thefirst hollow-core photonic-bandgap fiber is at an end of the firsthollow-core photonic-bandgap fiber.
 3. The device of claim 1, whereinthe twisted portion of the first hollow-core photonic-bandgap fiber isbetween two portions of the first hollow-core photonic-bandgap fiber. 4.The device of claim 3, wherein the two portions are non-twisted.
 5. Thedevice of claim 1, further comprising at least a portion of a secondhollow-core photonic-bandgap fiber optically coupled to the twistedportion of the first hollow-core photonic-bandgap fiber, wherein theportion of the second hollow-core photonic-bandgap fiber has a secondlongitudinal axis and is twisted about the second longitudinal axis. 6.The device of claim 5, wherein the twisted portion of the firsthollow-core photonic-bandgap fiber is twisted in a first direction aboutthe first longitudinal axis and the twisted portion of the secondhollow-core photonic-bandgap fiber is twisted in a second directionabout the second longitudinal axis, with the second direction generallyopposite to the first direction.
 7. The device of claim 5, wherein thefirst hollow-core photonic-bandgap fiber and the second hollow-corephotonic-bandgap fiber are the same hollow-core photonic-bandgap fiber.8. The device of claim 5, further comprising a single-mode fiberpositioned between and optically coupled to the twisted portion of thefirst hollow-core photonic-bandgap fiber and the twisted portion of thesecond hollow-core photonic-bandgap fiber.
 9. The device of claim 5,wherein the twisted portion of the first hollow-core optical fiber isbetween two non-twisted portions of the first hollow-corephotonic-bandgap fiber, and the twisted portion of the secondhollow-core photonic-bandgap fiber is between two non-twisted portionsof the second hollow-core photonic-bandgap fiber.
 10. The device ofclaim 5, wherein the twisted portion of the second hollow-corephotonic-bandgap fiber is twisted about the second longitudinal axisalong a second beat length of the twisted portion of the secondhollow-core photonic-bandgap fiber.
 11. The device of claim 10, whereinthe second beat length is substantially equal to the first beat length.12. The device of claim 10, further comprising at least a portion of athird hollow-core photonic-bandgap fiber optically coupled to thetwisted portion of the second hollow-core photonic-bandgap fiber,wherein the portion of the third hollow-core photonic-bandgap fiber hasa third longitudinal axis and is twisted about the third longitudinalaxis along a third beat length of the twisted portion of the thirdhollow-core photonic-bandgap fiber.
 13. The device of claim 12, whereinthe twisted portion of the first hollow-core photonic-bandgap fiber istwisted in a first direction about the first longitudinal axis, thetwisted portion of the second hollow-core photonic-bandgap fiber istwisted in a second direction about the second longitudinal axis, andthe twisted portion of the third hollow-core photonic-bandgap fiber istwisted in a third direction about the third longitudinal axis, thethird direction generally opposite to the first direction or generallyopposite to the second direction.
 14. The device of claim 12, whereinthe first hollow-core photonic-bandgap fiber, the second hollow-corephotonic-bandgap fiber, and the third hollow-core photonic-bandgap fiberare the same hollow-core photonic-bandgap fiber.
 15. The device of claim12, wherein the first beat length, the second beat length, and the thirdbeat length are approximately equal to one another.
 16. The device ofclaim 12, wherein at least one of the first beat length, the second beatlength, and the third beat length is not equal to the other beatlengths.
 17. The device of claim 1, wherein the wavelength is in therange between about 1545 nanometers and about 1550 nanometers.
 18. Thedevice of claim 1, wherein the first beat length is in the range betweenabout 1 centimeter and about 10 centimeters.
 19. The device of claim 1,wherein the twisted portion of the first hollow-core photonic-bandgapfiber has an amount of twisting which is configured to be varied.
 20. Amethod of modifying an optical signal, the method comprising: providingan optical signal having a first state of polarization; and propagatingthe optical signal through at least a portion of a hollow-corephotonic-bandgap fiber having a longitudinal axis and twisted about thelongitudinal axis along a beat length of the twisted portion of thehollow-core photonic-bandgap fiber such that the optical signal isoutputted from the twisted portion of the hollow-core photonic-bandgapfiber with a second state of polarization different from the first stateof polarization.
 21. The method of claim 20, further comprising varyingan amount of twisting of the twisted portion of the hollow-corephotonic-bandgap fiber about the longitudinal axis to select the secondstate of polarization.